Theorems · Theorem · group theory
Subgroup.exists_leftTransversal_of_FiniteIndex
∀ {G : Type u_1} [inst : Group G] {D H : Subgroup G} [D.FiniteIndex],
D ≤ H → ∃ t, Subgroup.IsComplement ↑t ↑(D.subgroupOf H) ∧ ⋃ g ∈ t, ↑g • ↑D = ↑H- Defined in
- Mathlib.GroupTheory.CosetCover
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupSubgroup.FiniteIndex
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Set.iUnionstatement and proof · cited by 2,483
- Set.extproof · cited by 2,266
- Set.Finiteproof · cited by 1,814
- Set.smulSetstatement · cited by 608
- Set.iUnion_congr_Propproof · cited by 374
- Set.Finite.toFinsetproof · cited by 351
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.leftCoset_cover_filter_FiniteIndex_auxproof · cited by 3